Of course, if one admits a wrong argument expressed in a superficially rational-looking form as a rational argument then one can come to anything through rational argument, but the claim to rationality depends on a willingness to see and acknowledge flaws in one's argument.

It is irrational to persist in believing arguments which have been shown to be incorrect, and it is only slightly less irrational to repeatedly fall for false arguments in favour of a proposition just because you want to have a "reason" to believe it.

Frankly, the only faith for which I have any respect is that which admits it is *not* supported by reason. If the existence of God were provable by reason then there would be no reason for faith and so to claim to have made an act of willful faith would itself be unreasonable. (Except perhaps if belief in god were attributed to faith in reason, which then sets reason above God - which may well be a greater sin than not believing in "him" at all.)

P.S. While it is not "irrational" to make a logical error it is arguably stupid to do so - and since (at least in my experience) we all make stupid mistakes quite frequently, I suspect that those who are offended by the charge of stupidity are displaying a higher level of arrogance than that of which they accuse their accusers.